Disparity in temporal and spatial relationships between resting-state electrophysiological and fMRI signals

Resting-state brain networks (RSNs) have been widely applied in health and disease, but the interpretation of RSNs in terms of the underlying neural activity is unclear. To address this fundamental question, we conducted simultaneous recordings of whole-brain resting-state functional magnetic resonance imaging (rsfMRI) and electrophysiology signals in two separate brain regions of rats. Our data reveal that for both recording sites, spatial maps derived from band-specific local field potential (LFP) power can account for up to 90% of the spatial variability in RSNs derived from rsfMRI signals. Surprisingly, the time series of LFP band power can only explain to a maximum of 35% of the temporal variance of the local rsfMRI time course from the same site. In addition, regressing out time series of LFP power from rsfMRI signals has minimal impact on the spatial patterns of rsfMRI-based RSNs. This disparity in the spatial and temporal relationships between resting-state electrophysiology and rsfMRI signals suggests that electrophysiological activity alone does not fully explain the effects observed in the rsfMRI signal, implying the existence of an rsfMRI component contributed by “electrophysiology-invisible” signals. These findings offer a novel perspective on our understanding of RSN interpretation.


Introduction
Sophisticated brain function requires coordinated activities from separate brain regions, collectively forming functional brain networks.Functional brain networks in humans and animals are predominantly studied using the method of resting-state functional magnetic resonance imaging (rsfMRI), which measures the synchronization of brain-wide spontaneous blood-oxygenlevel dependent (BOLD) signals.These networks are commonly referred to as resting-state brain networks (RSNs).
Despite the widespread application of BOLD-derived RSNs in both health and disease contexts, their relationship to the underlying neural activity remains incompletely understood.This is a fundamental issue, as the BOLD signal is known to indirectly reflect neural activity through accompanying hemodynamic and metabolic changes, a mechanism known as neurovascular coupling (NVC).While tight NVC has been repeatedly demonstrated when neural activities are evoked by explicit external stimulation (Goense and Logothetis, 2008;Logothetis et al., 2001;Nemoto et al., 2004), this relationship in the resting state remains elusive.There is considerable evidence indicating that the spatial patterns of most RSNs effectively mirror established functional systems and activation patterns observed during various tasks (Biswal et al., 1995;Glasser et al., 2016;Hampson et al., 2002;Lowe et al., 1998;Smith et al., 2009), as well as patterns of brain structural networks (Andrews-Hanna et al., 2010;Greicius et al., 2009;Lowe et al., 2008).In addition, alterations in RSNs have been documented in several brain disorders, aligning with neuropathophysiological changes (Buckner et al., 2009).This collective body of evidence suggests a robust neural basis for RSNs.However, it is notable that despite these findings, the predictive power of resting-state electrophysiological signals for corresponding rsfMRI time series is often relatively low (Mateo et al., 2017;Scholvinck et al., 2010;Winder et al., 2017), and some studies have even demonstrated a disconnection between neural activity and hemodynamic signals under specific conditions (Maier et al., 2008;Zhang et al., 2019).Moreover, various studies have reported divergent electrophysiological correlates of the rsfMRI signal across a broad spectrum of LFP bands, spanning from infraslow signals (Hiltunen et al., 2014;Pan et al., 2013) and low-frequency delta/sub-delta band signals (He et al., 2008;Lu et al., 2007) to highfrequency gamma band signals (Bastos et al., 2015;Foster et al., 2015;Keller et al., 2013;Mukamel et al., 2005;Nir et al., 2008;Magri et al., 2012), as well as spiking activity (Mukamel et al., 2005).These findings suggest that the rsfMRI signal may reflect diverse aspects of neural activity.Taken together, how RSNs and rsfMRI relate to spontaneous neural activity remains unclear (Laufs et al., 2003;Liu et al., 2011;Mantini et al., 2007), highlighting a significant gap in our understanding of functional brain networks.
To address this critical issue, we systematically investigated the role of electrophysiological activity in determining specific spatiotemporal patterns of BOLD-based RSNs.
In conjunction with whole-brain rsfMRI, we simultaneously recorded electrophysiology signals in the primary motor cortex (M1) and anterior cingulate cortex (ACC) in rats under light sedation and wakefulness.These brain regions were chosen due to their distinct roles in sensorimotor function and integrative cognition, respectively.Our data show that in both light-sedation and awake states, the spatial patterns of RSNs derived from gamma band power closely resemble BOLD-derived RSNs for both the M1 and ACC, and lower frequency band-derived RSNs exhibit inversed spatial patterns, both indicating strong neural underpinning of RSNs.However, the temporal profiles of band-limited LFP powers at both recording sites exhibit considerably lower temporal correlations with the corresponding local BOLD time courses.Moreover, regressing out the gamma band power or powers of all LFP bands has only limited effects on the spatial patterns of BOLD-derived RSNs, collectively suggesting LFP powers contribute only partially to the local rsfMRI signal.This disparity in spatial and temporal relationships between resting-state BOLD and electrophysiology signals implies that there might be an electrophysiology-invisible component of brain activity that significantly influences the rsfMRI signal and RSNs.

Results
To systematically analyze the spatiotemporal relationship between resting-state electrophysiology and fMRI signals, we conducted simultaneous recordings of whole-brain rsfMRI and electrophysiology signals in the M1 and ACC in rats under both light-sedation and awake states (Fig. 1A).The accuracy of electrode placement in the M1 and ACC was confirmed using T2-weighted structural images (Fig. S1).Raw electrophysiology data were initially preprocessed to remove MR artifacts using a template regression approach (Tu and Zhang, 2022).Subsequently, the LFP was extracted by bandpass filtering preprocessed electrophysiology data within the frequency range of 0.1 -300 Hz.An illustration of denoised LFP is depicted in Fig. 1A and Fig. S2.Band-specific LFP power was computed using a conventional LFP band definition .Figs. 1B-C illustrate the cross correlations between LFP power and BOLD signal in the M1 across the LFP spectrum (Fig. 1B, 1-Hz band interval) and for individual LFP bands (Fig. 1C).These data demonstrate that gamma band power is positively correlated with the BOLD signal, while lowerfrequency bands display negative peak correlations with the BOLD signal.Additionally, the lag of the BOLD signal is approximately 2 sec for all bands, consistent with the hemodynamic response function (HRF) delay previously reported in rodents (Scholvinck et al., 2010;Winder et al., 2017).

LFP and rsfMRI signals derive consistent RSN spatial patterns in lightly sedated rats.
We first examined the spatial relationship between brain-wide rsfMRI signals and frequency band-specific LFP powers in lightly sedated rats.For each recording site, its BOLDderived RSN was obtained as the seedmap, calculated by voxel-wise correlating the regionally averaged BOLD time series of the seed (M1 in Fig. 1F and ACC in Fig. 2B) with BOLD time series of individual brain voxels.This seedmap conventionally represents the resting-state functional connectivity (RSFC) pattern for the seed region.To assess the extent to which this RSN could be obtained using the LFP signal recorded from the same location (M1 or ACC), we convolved the power of each LFP band with a rodent-specific HRF (Fig. 1D, (Tong et al., 2019)) to generate the LFP band-predicted BOLD signal.Subsequently, we voxel-wise correlated this signal with the brain-wide rsfMRI signal, producing the LFP band-derived RSN map (Fig. 1E, Fig. 2A).Our findings revealed that the gamma band power-derived RSN map exhibited high spatial consistency with the corresponding BOLD-derived RSN map (i.e.seedmap).Specifically, for M1, the voxel-to-voxel Pearson correlation coefficient (CC) between the mean gamma-derived RSN map (Fig. 1E) and mean BOLD-derived RSN map (Fig. 1F) was 0.95 (Fig. 1K, R 2 = 0.90), indicating 90% of the variance in the M1 BOLD-derived RSN map could be explained by the gamma-derived map.Conversely, spatial maps generated by lower-frequency bands displayed inverse correlations with the M1 BOLD-derived RSN map, with a trend of increasingly negative spatial CC in lower-frequency bands (Figs.1E-J, delta: CC = -0.78;theta: CC = -0.78;alpha: CC = -0.5;beta: CC = -0.34),consistent with the LFP-BOLD cross correlations for these bands shown in Fig. 1B-C.These relationships are repeatable in the ACC (Figs. 2A-G, delta: CC = -0.62;theta: CC = -0.3;alpha: CC = -0.12;beta: CC = 0.12; gamma: CC = 0.85).These results suggest that the spatial patterns of BOLD-based RSNs can be reliably obtained using band-specific LFP signals.
To confirm that these findings were not an artifact of specific frequency cutoffs we adopted for any LFP band, we repeated the analysis for all individual 1-Hz bands across the full LFP spectrum.Once again, we observed a gradual transition from negative to positive spatial correlations in LFP-derived RSN maps with the corresponding BOLD-derived RSN maps as the LFP signal changed from low to high frequencies (Fig. 1L for M1; Fig. 2H for ACC).Additionally, as a control analysis, we temporally shuffled the gamma band power in the ACC, convolved it with the HRF and recalculated the correlation map (Fig. S3).As a result of this manipulation, the spatial pattern observed in Fig. 2A disappeared, suggesting that the observed LFP-derived spatial patterns were specifically related to the LFP signal, rather than an artifact of the HRF.We also confirmed that all our results are not sensitive to the rsfMRI data preprocessing step of global signal regression (Figs.S4-S5).
In summary, our data collectively indicate that BOLD-derived RSNs can be reliably replicated using LFP power from the same site in lightly sedated rats, underscoring the critical involvement of neural activity in RSN spatial patterns.the ACC LFP-derived RSN map for each band, quantified by their voxel-to-voxel spatial correlations (C: delta, CC = -0.62;D: theta, CC = -0.30;E: alpha, CC = -0.12;F: beta, CC = 0.12; G: gamma, CC = 0.85).H) Spatial correlations between the ACC BOLD-derived RSN map and RSN maps derived by individual 1-Hz bands across the full LFP spectrum.
Temporal correlation between LFP power and local rsfMRI signal is significant but considerably weaker.
Given that the gamma power-derived RSN map can explain ~90% of the spatial variance of the BOLD-derived RSN map (Fig. 1K, R = 0.95, R 2 = 0.90) when noise is diminished by averaging RSN maps across scans, we ask how much variance of the local BOLD time series the gamma power can explain without significant influence of noise.Although we cannot directly average rsfMRI/electrophysiology time courses across scans to reduce noise levels, we can estimate the true LFP-BOLD temporal correlation by quantitatively evaluating the effect of noise on correlation values.To achieve this aim, we utilized the difference between the spatial correlation of averaged M1 RSN maps (i.e.referred to as denoised data, R = 0.95, Fig. 1K) and that of unaveraged RSN maps (i.e.referred to as with-noise data, R = 0.58, Fig. 3A, gamma band power).Using this difference, we simulated two fixed signals with a true correlation of 0.95.By introducing varying levels of noise to the signals, we determined at what noise level the apparent correlation between the two signals became 0.58 (Fig. 3C).Specifically, in each trial, random noise at a defined contrast-noise-level (CNR) was added to the simulated signals, and this process was repeated 159 times (i.e.equal to the number of scans in our study) for a given CNR level.At each CNR level, the correlation was calculated based on either the averaged signals from all 159 trials (i.e.simulating denoised data, Fig. 3C), or the signals of individual trials (i.e.simulating with-noise data) before averaging resulting correlations across trials.
As anticipated, lower CNR values correspond to lower apparent trial-wise correlation values.Interestingly, we discovered that the trial-wise apparent correlation of 0.58, with the true correlation of 0.95, corresponds to the CNR of 1.3 (Fig. 3D-E), which aligns with the CNR of BOLD contrast reported in the literature (Atkinson et al., 2008).At this CNR level, we estimated that the true BOLD-LFP temporal correlation in the M1 should be approximately 0.59 (R 2 = 0.35, Fig. 3F-G), when the apparent correlation is 0.37 as measured by the gamma-BOLD temporal correlation in our real data (Fig. 3A).These findings indicate the temporal information provided by gamma power can only explain a minor portion (approximately 35%) of the temporal variance in the BOLD time series, even after accounting for the noise effect, which is in line with the reported correlation values between the cerebral blood volume (CBV) and fluctuations in GCaMP signal in head-fixed mice during periods of immobility (R = 0.63) (Ma et al., 2016).These results are also consistent with previous reports of relatively weak temporal correlations between gamma power and hemodynamic signals at rest obtained using different imaging modalities (Scholvinck et al., 2010;Winder et al., 2017).Furthermore, our simulation suggests that the difference in the number of data points (1200 in temporal correlation calculation vs. 6157 in spatial correlation calculation) has a negligible influence on correlation values (Figs.3D-G)., 5A).However, this regression process minimally altered M1/ACC BOLD-derived RSN maps (Figs.4B, 5B).This result remained consistent when the powers of all LFP bands were voxel-wise regressed out from rsfMRI signals using soft regression (Figs.4C, 5C).Soft regression was utilized to address the multicollinearity issue in the regression model resulting from potential correlations between LFP bands, as this method allows only unique components in five LFP bands to be regressed out.
To investigate whether the regression process is disproportionately dominated by time points with the largest LFP amplitude (i.e.outliers), we recalculated the M1/ACC BOLD-derived RSN maps after removing rsfMRI volumes corresponding to peaks in the M1/ACC gamma power (i.e.time points with the signal amplitude above the 85th percentile in HRF-convolved gamma power of each scan, Figs.4D, 4E & 5D).The spatial similarities between the BOLD-derived RSN maps before and after gamma power regression, all band power regression, or peak removal are summarized in Figs.4F & 5E, showing that the removal of gamma power has limited impact on the M1/ACC RSN maps.
To control for the potential nonlinear relationship between band-specific LFP powers and the rsfMRI signal, we calculated the mutual information between band-limited LFP powers and rsfMRI signals for all brain voxels (Fig. S7).The results show limited mutual information between any band-specific power and voxel-wise rsfMRI signals, indicating that the nonlinear component between BOLD and electrophysiological signals does not significantly influence RSN spatial patterns, which is consistent with the report that macroscopic resting-state brain dynamics are best described by linear models (Nozari et al., 2024).These data collectively indicate that the temporal fluctuations of LFP have limited effects on BOLD-derived RSN spatial patterns.

Disparity in temporal and spatial correlations persists across different physiological states.
To determine whether the disparity between temporal and spatial correlations of restingstate LFP and fMRI signals we observed is a specific phenomenon under anesthesia or can be generalized to different physiologic states, we repeated the experiment in awake rats.Despite that the physiological dynamics are substantially different, we still found higher spatial correlations between LFP-derived maps (Fig. S8A) and the BOLD-derived RSN map (Fig. S8B) in the M1.
Overall, both spatial and temporal correlations showed lower magnitudes in the awake state, likely due to increased variability from motion and other physiological fluctuations, as well as the smaller number of scans compared to the light sedation state (50 awake scans, 159 light-sedation scans for M1 and 172 light-sedation scans for ACC).Nonetheless, the consistent pattern of lower temporal but higher spatial correlations between gamma power and the rsfMRI signal supports the notion that this disparity is a general phenomenon across different physiological states.
The lack of significant alteration in BOLD-derived RSN maps after regressing out gammaband power or powers of all LFP bands in both ACC and M1 of awake rats (Fig. S11) further reinforces our earlier findings.These results indicate that the major findings observed in lightly anesthetized rats, including the disparity between temporal and spatial correlations, can be replicated in unanesthetized rats.Therefore, it appears that these results are not specific to the effects of anesthesia but rather reflect fundamental aspects of the relationship between electrophysiological and hemodynamic signals in the brain across different physiological states.

Ongoing rsfMRI signal could be contributed by electrophysiology-invisible brain activities.
Our findings indicate that the LFP signal can capture RSN patterns that account for nearly all the spatial variance observed in BOLD-based seedmaps.However, the temporal dynamics of the LFP signal only explain a minor fraction of the local BOLD time series and have minimal impact on the spatial patterns of BOLD-based RSNs.To reconcile this apparent contradiction, we propose a theoretical model, described as follows: Brain activity consists of components measurable by electrophysiology and others that are electrophysiology-invisible.In addition to the electrophysiology activity, electrophysiologyinvisible brain activities, such as those involving nNOS neurons and astrocytes, actively contribute to NVC and can exert a significant influence on the rsfMRI signal.During the resting state, these two components may not be synchronized, lowering temporal correlations between electrophysiology and rsfMRI signals.Another factor contributing to low LFP-BOLD temporal correlations could be neuromodulations from distal modulator nuclei (e.g.locus coerulues and/or basal forebrain), which exert strong vasoactive effects but may not proportionately affect electrophysiology activity.Moreover, the signaling of electrophysiology activities and that of electrophysiology-invisible are both constrained by the same anatomical pathways.This allows the two signals to generate similar RSN spatial patterns in parallel measured by the BOLD signal, which can reflect both direct and indirect anatomical connectivity.The model is summarized in Figs. 6 and S12, and further details will be discussed in the next section.

Discussion
BOLD-derived RSNs have been widely investigated in multiple species (Damoiseaux et al., 2006;Lu et al., 2012;Mantini et al., 2011) and have been applied in various physiological and pathological conditions.However, the neural mechanisms underlying RSNs and the rsfMRI signal remain incompletely understood.To shed more light on this issue, we conducted systematic analysis of simultaneously recorded electrophysiology and rsfMRI signals in both lightly anesthetized and awake animals.Our findings reveal that both electrophysiology and rsfMRI signals can generate highly consistent brain-wide RSN patterns.However, the temporal information of the LFP signal contributes only minimally to the local BOLD time series at the same recording site.These seemingly paradoxical findings, along with those reported in the literature, can potentially be reconciled by the theoretical model we propose, which suggests that RSNs may also arise from electrophysiology-invisible brain activities that play a significant role in NVC.
Together, our data and model offer a new perspective for interpreting the neural basis underlying the resting-state BOLD signal.
The spatial correspondence between BOLD-and electrophysiology-derived RSNs has been repeatedly reported across various physiological states and species using different methods.
Studies employing electroencephalography (EEG) or electrocorticography (ECoG) in humans have shown that RSNs derived from the power of multiple-site electrophysiological signals exhibit similar spatial patterns to classic BOLD-derived RSNs, such as the default-mode network (Hacker et al., 2017;Kucyi et al., 2018).This high spatial correspondence between rsfMRI and LFP signals can even be found at the columnar level (Shi et al., 2017).Similarly, simultaneous recordings of resting-state calcium and fMRI signals in awake rats have revealed highly consistent spatial patterns between calcium-and BOLD-associated RSNs (Ma et al., 2022).Moreover, voltagesensitive dye imaging in mice has unveiled comparable sensory-evoked and hemisphere-wide activity motifs represented in spontaneous activity in both lightly anesthetized and awake states (Mohajerani et al., 2013).Furthermore, in a more recent study by Vafaii and colleagues, overlapping cortical networks were identified using both fMRI and calcium imaging modalities, suggesting that networks observable in fMRI studies exhibit corresponding neural activity spatial patterns (Vafaii et al., 2024).These results align well with the notion that RSN spatial patterns are highly consistent with known functional systems and activation patterns observed in task-based studies (Biswal et al., 1995;Glasser et al., 2016;Hampson et al., 2002;Lowe et al., 1998;Smith et al., 2009), as well as patterns of structural networks (Andrews-Hanna et al., 2010;Greicius et al., 2009;Lowe et al., 2008).Taken together, previous studies and our data indicate that both electrophysiology and rsfMRI measurements can generate consistent RSN spatial patterns, strongly suggesting that the spatial structures of RSNs are dictated by neural activities.
Previous studies have also indicated that RSNs are likely constrained by axonal projections.For instance, consistent sensory-evoked and hemisphere-wide activity motifs in mice, as revealed using voltage-sensitive dye imaging, are defined by regional axonal projections (Mohajerani et al., 2013).Our previous work in awake rats further demonstrate spatial consistency between RSNs and anatomical connectivity patterns in thalamocortical networks (Liang et al., 2013).In the current study, we compared RSNs of M1 and ACC to their anatomical networks defined by the axonal projection patterns obtained from the Allen Brain Institute database (Fig. S13, (Oh et al., 2014)), illustrating that RSNs revealed by either the BOLD or LFP signal closely resemble the corresponding anatomical networks.It is important to note that RSNs measured by functional connectivity can reflect both direct and indirect connectivity and thus may not necessarily have identical spatial patterns as the corresponding anatomical networks (Honey et al., 2009).
In contrast to the seemingly strong LFP-BOLD relationship inferred from their high spatial correlations, we observed appreciably lower (yet significant) temporal correlations between the two signals from the same recording sites (M1 and ACC).Regressing out LFP powers has limited impact on RSN spatial patterns, reinforcing the notion that the contribution of temporal variations of the LFP signal to RSN spatial patterns is minor.These results are supported by previous research demonstrating weak but significant correlations between CBV changes and spontaneous gamma-band LFP or multiunit activity in awake, head-fixed mice (Winder et al., 2017).Importantly, persistent spontaneous fluctuations in CBV were observed even after blocking local neural spiking and glutamatergic input, as well as noradrenergic receptors, indicating that hemodynamic signal fluctuations may not dominantly reflect local ongoing electrophysiology activity (Winder et al., 2017).Comparably low temporal correlations between gamma-band power and the rsfMRI signal have been reported in monkeys (Scholvinck et al., 2010;Shmuel and Leopold, 2008).Additionally, data from our group show similarly low temporal correlations between spontaneous calcium peaks, a measure of neural spiking activity, and the rsfMRI signal in awake rats (Ma et al., 2022).Furthermore, Vafaii et.al. revealed notable differences in functional connectivity strength measured by fMRI and calcium imaging, despite an overlapping spatial pattern of cortical networks identified by both modalities (Vafaii et al., 2024).These findings collectively suggest that while the temporal correlation between electrophysiology and rsfMRI signals is significant, the effect size of this correlation might be small.This result appears to remain consistent even for infraslow LFP activity (<1 Hz).Our data show that in the M1, the temporal correlation between infraslow LFP power and the rsfMRI signal was 0.08, while both derived consistent RSN spatial patterns (spatial correlation = 0.7), in line with the report that RSNs can be derived from infraslow LFP activity (Li et al., 2022).It is noteworthy that these results differ from two earlier studies in isoflurane-anesthetized rats, which found the LFP power in the primary somatosensory cortex was highly correlated with BOLD fluctuations (Liu et al., 2011;Pan et al., 2011).This discrepancy may be attributed to brain-wide synchronization during burst suppression in deeply anesthetized states in those studies.
Why would electrophysiology and rsfMRI signals exhibit unmatched spatial and temporal correlations?Our model offers one possible scenario that can reconcile this discrepancy.It hypothesizes that a portion of the rsfMRI signal is driven by electrophysiology-invisible brain activities involved in NVC.LFP records various neural activities, such as synaptic potentials and voltage-gated membrane fluctuations, reflecting the input and local neural processing of a particular brain region.However, electrophysiology cannot measure activities from certain cell populations, while electrophysiology-invisible components can trigger vasoactive responses and significantly contribute to the rsfMRI signal.For instance, the electrical activity of nNOS neurons is not detectable by electrophysiology because the nNOS neuron population is very small, yet it strongly contributes to NVC.Chemogenetic or pharmacological stimulation of nNOS neurons causes vasodilation without detectable changes in LFP (Echagarruga et al., 2020).In addition, astrocytes, a type of glia cell, coordinate communication between neurons and blood vessels and play a crucial role in NVC.Astrocytes regulate vessel tone by releasing signaling molecules such as ATP, arachidonic acid metabolites and nitric oxide (Ladecola and Nedergaard, 2007;Mulligan and MacVicar, 2004;Murphy et al., 1993).Furthermore, astrocytes can alter the diameter of blood vessels by extending or retracting the endfeet wrapping around them (Mills et al., 2022;Niu et al., 2019).Optogenetic stimulation of astrocytes in transgenic mice without affecting neurons elicited a BOLD response, indicating that astrocyte activity alone can cause changes in the BOLD signal, independent of neuronal activity (Takata et al., 2018).Additionally, Uhlirova et al. conducted a study where they utilized optogenetic stimulation and two-photon imaging to investigate how the activation of different neuron types affects blood vessels in mice.They discovered that only the activation of inhibitory neurons led to vessel constriction, albeit with a negligible impact on LFP (Uhlirova et al., 2016).These studies collectively suggest electrophysiology-invisible activities can significantly drive the rsfMRI signal.Exclusively identifying all electrophysiology-invisible sources contributing to the rsfMRI signal is beyond the scope of this work.However, a key point is that as the resting state LFP and electrophysiology-invisible (and thus rsfMRI) signals reflect different components of brain activities, they can be minimally synchronized and display low temporal correlations.Another possible factor that can contribute to low BOLD-LFP temporal correlations is direct modulation of the vasculature from distant modulator nuclei (e.g.locus coerulues and/or basal forebrain).Some neuromodulators, such as norepinephrine (NE) (Bekar et al., 2012;Kim et al., 2016) and acetylcoline (Ach) (Sato and Sato, 1995), have vasoconstrictive/vasodilatory effects that are spatially targeted in distributed brain regions, and thus can modulate brain-wide rsfMRI signals.However, these neural modulation effects may not be proportionately reflected from the electrophysiology signal, lowering BOLD-LFP temporal correlations (see a schematic diagram in Fig. S12).On the other hand, as the signaling of LFP-and electrophysiology-invisible components in functional networks is constrained by the same anatomical connectivity structure (Liu et al., 2018a;Liu et al., 2018b), the LFP-and BOLD-derived RSN spatial patterns can be highly similar and thus have high spatial correlations.
Our model can also potentially explain high spatial and temporal correlations when brain activation is evoked by external stimulation (Winder et al., 2017).At the evoked state, both LFP (and spiking activity) and electrophysiology-invisible components are temporally modulated by the same external stimulation paradigm, leading to both high temporal and high spatial correlations between fMRI and electrophysiology signals.

Potential pitfalls
Our proposed theoretic model represents just one potential explanation for the apparent discrepancy in temporal and spatial relationships between resting-state electrophysiology and BOLD signals.It is important to acknowledge that there may be other scenarios where a stronger temporal relationship between LFP and BOLD signals could manifest.For instance, recent research suggests that the relationship between LFP and rsfMRI signals may vary across different modes or instances (Cabral et al., 2023), which can be masked by correlations across the entire time series.Moreover, the 1-second temporal resolution employed in our study may obscure certain temporal correlations between LFPs and rsfMRI signals.Future investigations employing ultrafast fMRI imaging coupled with dynamic connectivity analysis could offer a more nuanced exploration of BOLD-LFP temporal correlations at higher temporal resolutions (Bolt et al., 2022;Thompson et al., 2014;Ma and Zhang, 2018).
In addition to LFP, various other features can be derived from electrophysiology signals and alternative methods for comparing electrophysiology and rsfMRI signals, such as rank correlation, warrant consideration.It is plausible that employing different features or comparison methods could yield a stronger BOLD-electrophysiology temporal relationship (Ma et al., 2016).
In our current study we focused solely on band-limited LFP power as the primary feature in our analysis, given its prevalence in prior studies of LFP-rsfMRI correlates.More importantly, we demonstrate that band-specific LFP powers can yield spatial patterns nearly identical to those derived from rsfMRI signals, prompting a closer examination of the temporal relationship between these same features.Furthermore, since correlational analysis was used in studying the LFP-BOLD spatial relationship, we used the same analysis method when comparing their temporal relationship.Some other comparison methods such as rank correlation and transformation prior to comparison were also tested and results remain persistent (Fig. S14).These findings align with the notion that, compared to nonlinear models, linear models offer superior predictive value for the rsfMRI signal using LFP data, as comprehensively illustrated in (Nozari et al., 2024) (also see Fig. S7).Importantly, in this study, the predictive powers (represented by R 2 ) of various comparison methods tested all remain below 0.5 (Nozari et al., 2024), suggesting that while certain models may enhance the temporal relationship between LFP and BOLD signals, the improvement is likely modest.Further exploration involving the extraction of all possible features from electrophysiology signals and their examination in relation to the rsfMRI signal, as well as the exploration of alternative methods for comparing LFP and rsfMRI signals warrants more detailed analysis in future studies.

Summary
Our study demonstrates that BOLD-based RSNs can be reliably derived by the electrophysiology signal.Nonetheless, the weak BOLD-LFP temporal correlations suggest that the dominant contributors to these networks might be signals not captured by electrophysiology.
This finding provides a novel interpretation of RSNs.Importantly, this new concept of RSN signaling does not in any way diminish the importance of BOLD-based RSNs or the rsfMRI method.In fact, it makes fMRI even more important than previously thought because it might provide a new signal that traditional electrophysiology measures cannot provide.

Animals
All experiments in the present study were approved by and conducted in accordance with guidelines from the Pennsylvania State University Institutional Animal Care and Use Committee (IACUC).Adult male Long-Evans rats weighing 300-500g were obtained from Charles River Laboratory (Wilmington, MA).Animals were housed in Plexiglas cages with food and water given ad libitum.The ambient temperature was maintained at 22-24°C under a 12h light :12h dark cycle.

Surgery
MR-compatible electrodes were implanted in animals with aseptic stereotaxic surgeries.The rat was briefly anesthetized with isoflurane before receiving intramuscular injections of ketamine (40 mg/kg) and xylazine (12 mg/kg).Baytril (2.5mg/kg) and long-acting buprenorphine (1.0mg/kg) were administered subcutaneously as antibiotics and analgesics, respectively.The animal was then endotracheal incubated and ventilated with oxygen using the PhysioSuite system (Kent Scientific Corporation).Body temperature was monitored and maintained at 37 °C with a warming pad placed underneath the animal (PhysioSuite, Kent Scientific Corporaition).Heart rate and SpO2 were continuously monitored using a pulse oximetry (MouseSTAT® Jr, Kent Scientific Corporation) throughout the surgery.After performing craniotomies over the right ACC (coordinates: anterior/posterior +1.5, medial/lateral +0.5, dorsal/ventral -2.8) and the left M1 (coordinates: anterior/posterior +3.2, medial/lateral -3, dorsal/ventral -2.8), two MR-compatible electrodes (MRCM16LP, NeuroNexus Inc) were carefully implanted into the ACC and M1, respectively.The reference and grounding wires from each electrode were wired together and connected to one of the two silver wires placed in the cerebellum.This electrode, which is a silicon-based micromachined probe, is capable of recording the LFP activity within a broad frequency range, starting from 0.1Hz.At last, the skull was sealed with dental cement.After surgery, the animal was returned to the homecage and allowed to recover for at least one week before any experiment.

Acclimation for awake imaging
Rats were restrained using a custom-designed restrainer during awake imaging sessions.To minimize stress and motion during the imaging process, animals underwent a 7-day acclimation procedure to the restrainer as well as the MRI environment and scanning noise.The duration of the acclimation procedure was gradually increased from 15 min on the first day to 60 min on days 4-7 days (i.e., 15 min on day 1, 30 min on day 2, 45 min on day 3, and 60 min on days 4-7).More details of the acclimation procedure can be found in previous publications from our laboratory (Liang et al., 2012) and other research groups (Bergmann et al., 2016;Chang et al., 2016).

Simultaneous rsfMRI and electrophysiology recordings
All rsfMRI experiments were conducted on a 7T Bruker 70/30 BioSpec system running ParaVision 6.0.1(Bruker,Billerica, MA) using a homemade single loop surface coil at the high field MRI facility at the Pennsylvania State University.During each fMRI session, T2*-weighted rsfMRI images covering the entire brain were obtained using an echo planar imaging sequence with the following parameters: repetition time (TR) = 1 s; echo time (TE) = 15 ms; field of view = 3.2 × 3.2 cm 2 ; matrix size = 64 × 64; slice number = 20; slice thickness = 1mm; volume number = 1200.Five to ten scans were repeated within each session.T2-weighted anatomical images were also acquired using a rapid acquisition with a relaxation enhancement (RARE) sequence with the following parameters: TR = 3000 ms; TE= 40 ms; field of view = 3.2 × 3.2 cm 2 ; matrix size = 256 × 256; slice number = 20; slice thickness = 1 mm; repetition number = 6.
Six rats with two electrodes implanted in the ACC and M1 were imaged in both awake and lightly sedated states in separate fMRI sessions.Two additional rats with an electrode only implanted in the ACC were imaged in the light sedation state.For both states, animals were restrained throughout the imaging session.In the light sedation state, the animal was sedated with the combination of low-dose dexmedetomidine (initial bolus of 0.05 mg/kg followed by a constant infusion at the rate of 0.1 mg•kg −1 •h −1 ) and low-dose isoflurane (0.3%).Artificial tears were applied to protect the animal's eyes from drying out.Body temperature was maintained at 37°C using warm air and was monitored using a rectal thermometer.
Before imaging, the implanted electrodes were connected to MR-compatible LP16CH headstages and a PZ5 neurodigitizer amplifier (Tucker Davis Technologies (TDT) Inc, Alachua, FL).Electrophysiology recording began 10 min before rsfMRI data acquisition and continued until the end of the imaging session using a TDT recording system and an RZ2 BioAmp Processor (TDT Inc, Alachua, FL).The raw, unfiltered electrophysiology signal was sampled at 24414 Hz and stored using the TDT Synapse software on a WS8 workstation.rsfMRI and electrophysiology data preprocessing when multiple regressors are involved particularly when regressors are correlated between themselves.Lastly, we removed rsfMRI volumes corresponding to peaks in the M1/ACC gamma power.The seedmaps of M1 and ACC were recalculated and compared before and after removing the LFP signal.

Simulation
We simulated two fixed signals with the true Pearson correlation of 0.95.The first signal was generated using MATLAB function rand with 10000 data points.The second signal with a defined correlation with the first signal (i.e.0.95) was obtained based on the equation below:  = A * Corr + �1 −  2 * (0,1) in which A represents the first signal, Corr is the desired Pearson correlation coefficient, and N(0, 1) represents random values with the mean equal to 0 and standard deviation equal to 1.For each signal, random noise was added to achieve a contrast-to-noise ratio (CNR) ranging from 0.1 to 5 with the step size of 0.1.CNR was quantified by the standard deviation of the signal over the standard deviation of the noise.This process was repeated 159 times (equal to the # of scans in the present study).The noise-added signals were resampled to either 1200 or 6157 data points, which corresponded to the total number of time points used to calculate temporal correlations and total number of brain voxels used to calculate spatial correlations, respectively, in our study.

Figure 1 .
Figure 1.Highly consistent RSN spatial patterns derived from LFP and rsfMRI signals in the M1 of lightly sedated rats.A) Simultaneous acquisition setup for whole-brain rsfMRI and electrophysiology signals in the M1 and ACC.B) Cross correlations between the rsfMRI signal and LFP power in the M1 across the frequency range of 0.1-100 Hz (band interval: 1Hz; lag range: -20 -20 s.C) Cross correlations between the rsfMRI signal and powers of individual LFP bands in the M1.Error bars: SEM.D) Exemplar powers of individual LFP bands.Convolving these powers with a rodent-specific hemodynamic response function (HRF) generates the

Figure 2 .
Figure 2. Highly consistent RSN spatial patterns derived from LFP and rsfMRI signals in the ACC of lightly sedated rats.A) ACC band-specific LFP power-derived RSN maps, obtained by voxel-wise correlating the LFP-predicted BOLD signal for each band with BOLD signals of all brain voxels.B) ACC BOLD-derived RSN map (i.e.ACC seedmap), obtained by voxel-wise correlating the regionally averaged BOLD time course of the seed (i.e.ACC) with BOLD time courses of all brain voxels.C-G) Spatial similarity between the ACC BOLD-derived RSN map and Figure 3. Disparity in spatial and temporal correlations persists after controlling for the noise effect.A, B) Comparison of scan-wise spatial and temporal correlations (paired t-tests across individual scans.***:p<0.005).C-G) Simulation to evaluate factors affecting apparent correlation values including contrast-to-noise ratio (CNR) and the number of data points; C) Two

Figure 4 .
Figure 4. Impact of removing the electrophysiology signal on M1 BOLD-derived RSN spatial patterns.A) RSN map derived from gamma power after regressing out the HRFconvolved gamma power in the M1 from rsfMRI signals of all brain voxels.B) M1 BOLD-derived RSN map (i.e.M1 seedmap) after voxel-wise regression of the HRF-convolved gamma power from rsfMRI signals.C) M1 BOLD-derived RSN map after voxel-wise regression of all five LFP band powers from rsfMRI signals using soft regression.D) Peaks of HRF-convolved gamma power in one representative scan.E) M1 BOLD-derived RSN map after removing 15% of rsfMRI time points corresponding to gamma peaks.F) Spatial similarity of M1 BOLD-derived RSN maps

Figure 6 .
Figure 6.A theoretic model that can explain the disparity in spatial and temporal correlations between resting-state electrophysiology and fMRI signals.
Pearson correlations between the resampled signals either based on the averaged signals from all 159 trials or on individual trials were calculated.Author Contributions: N.Z.designed the research; W.T. performed animal experiments; W.T. performed data analysis; S.R.C. designed and made the restrainer for imaging experiments; W.T. and N.Z.wrote the paper; W.T., S.R.C. and N.Z.revised the paper; N.Z.acquired funding.